Andreev scattering and Josephson current in a one-dimensional electron liquid

Abstract

Andreev scattering and the Josephson current through a one-dimensional interacting electron liquid sandwiched between two superconductors are re-examined. We first present some apparently new results on the non-interacting case by studying an exactly solvable tight-binding model rather than the usual continuum model. We show that perfect Andreev scattering (i.e. zero normal scattering) at the Fermi energy can only be achieved by fine-tuning junction parameters. We also obtain exact results for the Josephson current, which is generally a smooth function of the superconducting phase difference except when the junction parameters are adjusted to give perfect Andreev scattering, in which case it becomes a sawtooth function. We then observe that, even when interactions are included, all low energy properties of a junction (E<<Δ, the superconducting gap) can be obtained by "integrating out" the superconducting electrons to obtain an effective Hamiltonian describing the metallic electrons only with a boundary pairing interaction. This boundary model provides a suitable starting point for bosonization/renormalization group/boundary conformal field theory analysis. We argue that total normal reflection and total Andreev reflection correspond to two fixed points of the boundary renormalization group. For repulsive bulk interactions the Andreev fixed point is unstable and the normal one stable. However, the reverse is true for attractive interactions. This implies that a generic junction Hamiltonian (without fine-tuned junction parameters) will renormalize to the normal fixed point for repulsive interactions but to the Andreev one for attractive interactions. An exact mapping of our tight-binding model to the Hubbard model with a transverse magnetic field is used to help understand this behavior.

revtex, 17 pages, 5 postscript figures

References in corpus (3)

• Magnetization Plateaux in N-Leg Spin Ladders
• Edge Magnetic Field in the xxz Spin-1/2 Chain
• Fermi Edge Singularities: Boundstates and Finite Size Effects

Cited by in corpus (86)

• Spintronics: Fundamentals and applications
• Semiconductor Spintronics
• Josephson and Andreev transport through quantum dots
• Josephson Current through a correlated quantum level: Andreev states and Pi-junction behavior
• Self-consistent description of Andreev bound states in Josephson quantum dot devices
• Spectral properties of locally correlated electrons in a BCS superconductor
• Quantum entanglement in carbon nanotubes
• Universal transport signatures of Majorana fermions in superconductor-Luttinger liquid junctions
• Junctions of three quantum wires
• Quantum transport through carbon nanotubes: proximity induced and intrinsic superconductivity
• Numerical Renormalization Group Approach to a Quantum Dot Coupled to Normal and Superconducting Leads
• Kondo effect in asymmetric Josephson couplings through a quantum dot
• Influence of the Rashba effect on the Josephson current through a superconductor/Luttinger liquid/superconductor tunnel junction
• Time-dependent quantum transport with superconducting leads: a discrete basis Kohn-Sham formulation and propagation scheme
• Parity measurement in topological Josephson junctions
• Topological Superconductor-Luttinger Liquid Junctions
• Spin-dependent transport in a Luttinger liquid
• The Josephson current in Luttinger liquid-superconductor junctions
• Andreev Transport through Side-Coupled Double Quantum Dots
• Spectroscopy of spin-split Andreev levels in a quantum dot with superconducting leads
• Interplay between Josephson effect and magnetic interactions in double quantum dots
• Yu-Shiba-Rusinov states in real metals
• Geometrical enhancement of the proximity effect in quantum wires with extended superconducting tunnel contacts
• Interplay between Kondo and Andreev-Josephson effects in a quantum dot coupled to one normal and two superconducting leads
• Signatures of topological phase transitions in Josephson current-phase discontinuities
• Effective Boundary Field Theory for a Josephson Junction Chain with a Weak Link
• Persistent currents in Dirac fermion rings
• The two-boundary sine-Gordon model
• Correlated electron transport through double quantum dots coupled to normal and superconducting leads
• Josephson effect through a quantum dot array
• Keldysh study of point-contact tunneling between superconductors
• Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction
• Josephson Currents in Quantum Hall Devices
• Equilibrium and time-dependent Josephson current in one-dimensional superconducting junctions
• Fractional Josephson Effect in Number-Conserving Systems
• Transport properties of topological superconductor-Luttinger liquid junctions: a real-time Keldysh approach
• Transfer matrix approach to the persistent current in hybrid normal-superconducting rings
• Pair excitations of a quantum spin on a proximitized superconductor
• Screening Clouds and Majorana Fermions
• Berry curvature tomography and realization of topological Haldane model in driven three-terminal Josephson junctions
• Josephson current through a long quantum wire
• From Cooper pair splitting to the non-local spectroscopy of a Shiba state
• Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems
• Boundary Field Theory Approach to the Renormalization of SQUID Devices
• Charge and Spin Effects in Mesoscopic Josephson Junctions
• One-dimensional transport of bosons between weakly linked reservoirs
• Quantum circuits with multiterminal Josephson-Andreev junctions
• A Twisted Ladder: relating the Fe superconductors to the high $T_c$ cuprates
• Josephson effect in a Fibonacci quasicrystal
• Magnetic-Field-Induced Transition in a Quantum Dot Coupled to a Superconductor
• Tunable Kondo screening length at a Y-junction of three inhomogenous spin chains
• Double-gap superconducting proximity effect in nanotubes
• Thermodynamic Bethe Ansatz for boundary sine-Gordon model
• The dc Josephson current in a long multi-channel quantum wire
• Andreev current in finite sized carbon nanotubes
• Metamorphosis and Taxonomy of Andreev Bound States
• Cooper-pair transport through a Hubbard chain sandwiched between two superconductors: Density matrix renormalization group calculations
• Charge-Kondo Effect in Mesoscopic Superconductors Coupled to Normal Metals
• Ground state phase diagram and "parity flipping'' microwave transitions in a gate-tunable Josephson Junction
• Superconducting proximity effect on a two-dimensional Dirac electron system
• Exact interacting Green's function for the Anderson impurity at high bias voltages
• Supercurrent transport through 1$e$-periodic full-shell Coulomb islands
• Detecting Majorana fermions by use of superconductor-quantum Hall liquid junctions
• Theory of a Single Magnetic Impurity on a Thin Metal Film in Proximity to a Superconductor
• Detecting a quantum critical point in topological SN junctions
• Spin-orbit coupling and proximity effects in metallic carbon nanotubes
• Tunneling Density of States, Pair Correlation, and Josephson Current in Spin-Incoherent Luttinger Liquid-Superconductor Hybrid Systems
• Nonmonotonic behavior of resistance in a superconductor-Luttinger liquid junction
• Generalized transmon Hamiltonian for Andreev spin qubits
• Currents and correlations in Luttinger liquids and carbon nanotubes at finite temperature and size: a bosonization study
• Yu-Shiba-Rusinov states, the BCS-BEC crossover, and the exact solution in the flat-band limit
• Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade
• DC Josephson Effect in a Tomonaga-Luttinger Liquid
• Stationary transport in mesoscopic hybrid structures with contacts to superconducting and normal wires. A Green's function approach for multiterminal setups
• Modeling long imperfect SNS junctions and Andreev bound states using two impurities and the T -matrix formalism
• Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor
• dc Josephson Effect in Metallic Single-Walled Carbon Nanotubes
• Josephson $\pi$-state in superconductor-Luttinger liquid hybrid systems
• Junctions of Spin-Incoherent Luttinger Liquids with Ferromagnets and Superconductors
• AC Josephson current and supercurrent noise through one-dimensional correlated electron systems
• Effect of Disorder on the Conductance of (non-) Topological SN Junctions
• SNS Junctions along the BCS-BEC Crossover
• Local Density of States in a Helical Tomonaga-Luttinger Liquid of Loop and Josephson Junction Geometries
• Andreev molecule in parallel InAs nanowires
• Quantum theory of an atom in proximity to a superconductor
• The contact conductance of a one-dimensional wire partly embedded in a superconductor